Unit 2 Lesson 9-Rate of Change
Unit 2 Lesson 9
Average Rate of Change
Objectives:
*I can find the average rate of change.
*I can compare the average rates of change.
Unit 2 Lesson 9-Rate of Change
Warm Up:
The table below compares the number of hours a cashier works
to her total earnings, in dollars. Write a linear equation to
represent the cashier's earnings and then graph it.
Cashier's Earnings
Time in hours, x
Earnings in $, y
0
0
2
15
4
30
Unit 2 Lesson 9-Rate of Change
Think back...what do you remember about slope?
Unit 2 Lesson 9-Rate of Change
shows how one quantity changes relative
to another quantity.
To calculate rate of change between two points (x1, y1) and (x2, y2)
use the formula:
Unit 2 Lesson 9-Rate of Change
Let's go back to our warm up problem...
Choose two ordered pairs, and find the average rate of change.
Cashier's Earnings
Time in hours, x
Earnings in $, y
0
0
2
15
4
30
Do you see any connection
to the rate of change and
the equation we wrote?
Unit 2 Lesson 9-Rate of Change
Let's Try...
Choose a pair of points on the graph in your notes and find the
average rate of change between them.
Determine the average rate of change between (-3, 7) and (4, 2)
Unit 2 Lesson 9-Rate of Change
You Try...
Find the average rate of change between (19, 0) and (-2, -5)
Unit 2 Lesson 9-Rate of Change
You Try...
Find the average rate of change between (8, -8) and (-1, -4)
Unit 2 Lesson 9-Rate of Change
Can we find the rate of change from a graph?
Unit 2 Lesson 9-Rate of Change
* What is the formula we use to find the rate of
change?
*What is another name for rate of change?
*Find the rate of change between (2,5) and
(-1, 3).
Unit 2 Lesson 9-Rate of Change
Let's Try...
A basketball championship begins with 64 teams. Every time a team wins a
game, it goes on to the next round. Once a team loses a game it is eliminated
from competition and does not play any more games. The number of teams in
each round of the championship is a function of the round. That function is
represented on the graph in your notes.
Compare the rate of change between rounds 1 and 2 to the
rate of change between rounds 2 and 3.
Unit 2 Lesson 9-Rate of Change
You Try...
Graph f(x) = 2x + 1. Find the average rate of change between any 2
consecutive x values.
Rate of change:
Compare your rate of change with someone near you.
What do you notice?
Unit 2 Lesson 9-Rate of Change
Let's look at the rate of change of a
LINEAR FUNCTION.
x
0
1
2
f(x)
What do you notice?
What part of a linear equation is rate of change?
3
Unit 2 Lesson 9-Rate of Change
Remember....
An exponential function has a graph that is a curve.
An exponential growth function is always __________ ,
while an exponential decay function is always
_________ .
x
f(x)
0
1
2
3
Unit 2 Lesson 9-Rate of Change
Let's Try...
Find and describe the average rate of change for four consecutive pairs of
values in the table.
x
-3
-2
-1
0
1
f(x)
64
16
4
1
1/4
Unit 2 Lesson 9-Rate of Change
Let's Try...
Determine the average rate of change between 3 consecutive pairs of points for
the function f(x) = -3x + 2.
x
f(x)
What type of function is this?
Unit 2 Lesson 9-Rate of Change
You Try...
Find the average rate of change for 3 intervals of f(x).
x
f(x)
-1
1/3
0
1
1
3
2
9
What type of function is this?
Unit 2 Lesson 9-Rate of Change
Compare the rates of change for f(x) = 10x
and function g, represented in the table.
x
What is the same?
*
*
*
g(x)
-1
1/8
0
1
1
8
2
64
3
512